A complex number Z satisfies |Z-(-2+2sqrt(3)i)|

Question

A complex number Z satisfies |Z-(-2+2sqrt(3)i)|<=2

anonymous · Answer

Find the least psosible values of |Z| 
so Z is going to be a circle 
(x+2)^2+(y-2sqrt(3))^2<=2

anonymous · Answer

(x+2)^2+(y-2sqrt(3))^2<=2^2 * 

how do i find the point clsoest to origin?

sirm3d · Answer

algebra-wise, this point (x,y) lies in the intersection of the line through the origin and $$\left( -2,2\sqrt{3} \right)$$ and the circle of radius and and center at $$\left( -2,2\sqrt{3} \right)$$

sirm3d · Answer

the radius of the circle is two

anonymous · Answer

hm why is the shortest from the origin to centre of circle?

anonymous · Answer

hi?

sirm3d · Answer

i didn't get the "why" question

anonymous · Answer

what you saying is that the point Z closest to the Origin is the point of intersection of the line from origin to centre of circle right

sirm3d · Answer

right

sirm3d · Answer

one point of intersection is nearest the origin, the other is farthest

anonymous · Answer

why what is your reasoning for that?

anonymous · Answer

HII REPLY

sirm3d · Answer

that's a fact from analytic geometry, unless you haven't taken up that course

anonymous · Answer

nope

anonymous · Answer

im in high school!

sirm3d · Answer

how about geometry? not yet?

anonymous · Answer

im not sure.. can you do a quick show?

sirm3d · Answer

|dw:1351757947870:dw|
will this suffice?

anonymous · Answer

hmm yeah|dw:1351758289910:dw|

anonymous · Answer

oh so.. shortest dist between a point and a circle is always going to be line perpendicular to tangent at any point

anonymous · Answer

or something like that..

sirm3d · Answer

yes

anonymous · Answer

what about find the greatest posible value of Arg(Z)